# Choosing the Dirichlet prior in a mixture model

Consider the following mixture model with $$K < \infty$$ components, $$f\left(x \mid \theta_{1}, \ldots, \theta_{K}, \pi_{1}, \ldots, \pi_{K}\right)=\sum_{k=1}^K \pi_{k} \varphi\left(x \mid \theta_{k}\right)$$ Here $$\theta$$ represent probability vectors (the component densities are multinomial). I want to do Bayesian inference and estimation via Gibbs sampling. I use Dirichlet priors for both $$\theta$$ and $$\pi$$, but want them as uninformative as possible. However, it seems that non-informative priors with mixture models should not be used (see e.g. page 2 here). I also understand it applies to both $$\omega$$ and $$\theta$$.

What would be adequate choices for the concentration parameters $$\alpha_1,\dots,\alpha_K$$ of the Dirichlet distribution for $$p(\theta)$$ and $$p(\omega)$$ here? Initially I wanted to impose $$\alpha_1=\cdots=\alpha_K=1$$ on $$p(\theta)$$ (and similarly for $$\theta$$) but I am not sure anymore.